Lecture 12 : Graph Laplacians and Cheeger ’ s Inequality
نویسنده
چکیده
Maybe the most beautiful connection between a discrete object (graph) and a continuous object (eigenvalue) comes from a concept called the Laplacian. It gives a surprisingly simple and algebraic method for splitting a graph into two pieces without cutting too many edges. In a sense, we take an NP-Complete problem of partitioning a graph and relax it to an easy to solve problem of finding an eigenvector of a certain type of matrix. The resulting partition is not optimal, but close to it in a certain provable sense. The algorithm is very practical and modifications of it are widely used for clustering objects into similar groups.
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